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Richard asks…
how far must an extension ladder extend above the roof line to be safe?
Aaron answers:
Depends, are you stepping out onto the roof? If so, you will need to have sufficient ladder to hold onto while stepping.
If all you’re doing is reaching the eaves, you just need enough to provide a solid landing on the roof edge. I’d never want less than a foot.
Make sure you have a level, solid base, and the recommended 4 to 1 slope on the ladder (roughly 1 ft out for every foot out from the wall, no more, no less)
George asks…
Help with an extension ladder question.?
ladder adjusts from 10 feet to 16 feet. suppose you lean it against a house at its minimum length. It touches the house 9 feet above the ground. without moving the base how high will the ladder reach when extended
Aaron answers:
Distance of foot of ladder from house
= √(10² – 9²) = √(100 – 81) = √19
Height when extended
= √(16² – (√19)²) = √(256 – 19) = √237 = 15.39 ft
Donna asks…
SIN TAN COS MATH HELP?
There is an extension ladder that can extend out to 20 feet. When they put the ladder against the wall it makes a 70 degree angle. How far up the can the ladder reach?
What I did was Sin70x20 = 18.8 feet up the wall (Which I am unsure of, which is why I am here)
Aaron answers:
This is good if it makes a 70* angle with the ground.
But it sounds like the ladder makes the angle with the wall.
In that case use cosine. X = 6.84 ft
Maybe you have a picture?
Hope this helps!
Mary asks…
10th Grade Math? Be the first to help me.. 
?
When an extension ladder rests against a wall it reaches 4m up the wall. The ladder is extended a further 0.8 m without moving the foot of the ladder now it rests against the wall 1m further up. How long is the extended ladder?
Please show all your work. Thanks
Aaron answers:
Set up a right triangle – 1m on one side, b represents the unknown side parallel to the ground, and the hypotenuse is 0.8m
using pythagorean theorem, side b = 0.6m
because the whole ladder is also a right triangle, you can find the distance from the wall to the foot of the ladder by using:
4m/1m = 0.6m/distance from wall to foot of ladder
doign this, the distance = 0.15m
again, using pytahgorean theorem, the hypotenuse equals the lenght of the extended ladder, which is 5.002m
William asks…
Trigonometry question with ladders…?
When an extension ladder rests against a wall it reaches 4m up the wall. The ladder is extended a further 0.8m without moving the foot of the ladder and it now rests against the wall 1m further up. Find:
a. the length of the extended ladder.
b. the increase in the angle that the ladder makes with the ground now that the ladder is extended.
[I don't just want answers! I want to know how you did it. D: ]
I have already tried using elimination, substitution, and equating two different equations to try to find out what one of the sides was, but it didn’t work…
I really do not see how this works. If you get (L – 0.8)^2 – L^2 = 5^2 – 4^2 wouldn’t you get L^2 – 0.64 – L^2 on one side which completely cancels out L?
Oh, geez. I can be such an idiot some times. D< I completely forgot that (L + 0.8)^2 meant (L + 0.8)(L + 0.8), thus I forgot to expand. *Rolls eyes* Thank you for all the help!
Aaron answers:
Let x = length of ladder
x + 0.8 = length of ladder extended
d = distance of foot of ladder from wall
d² = x² – 4²
d² = (x + 0.8)² – 5²
(x + 0.8)² – 5² = x² – 4²
x² + 1.6x + 0.64 – 25 = x² – 16
1.6x = – 16 + 25 – 0.64
1.6x = 8.36
x = 8.36/1.6 = 5.225 m length of ladder
x + 0.8 = 6.025 m length of extended ladder.
θ₁ = sinˉ (4/5.225) = 49.99559686° ≈ 50°
θ₂ = sinˉ (5/6.025) = 56.08595289° ≈ 56°
θ₂ – θ₁ = 56° – 50° = 6° increase in angle
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